Tight sandstone gas reservoir numerical simulation method considering reservoir parameter time variation

Abstract

The invention belongs to the technical field of tight sandstone gas reservoir numerical simulation, and particularly relates to a tight sandstone gas reservoir numerical simulation method considering reservoir parameter time varying, which comprises the following steps of: based on commercial numerical simulation software, combining stress sensitivity and gas-water two-phase permeability experiment results, deducing and coupling through a model, and obtaining a gas-water two-phase permeability model; and establishing a tight sandstone gas reservoir numerical simulation method considering complex seepage mechanisms such as stress sensitivity and relative permeability time variation. Due to the fact that changes of stress sensitivity and gas-water relative permeability under the real reservoir condition are considered in the simulation process, the change rules of the yield, the formation pressure and the water saturation in the actual production process can be truly reflected. The method has the advantages of being easy to apply, wide in application range and accurate in result, and a theoretical basis is provided for analyzing the gas well yield change rule and formulating a development scheme.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical simulation of tight gas reservoirs, and particularly relates to a numerical simulation method for tight sandstone gas reservoirs considering the time-varying reservoir parameters. Background Art

[0002] The proportion of tight gas in oil and gas reserves and production has been increasing year by year, becoming one of the unconventional natural gas resources with the largest development scale at present. Most of the tight sandstone gas reservoirs discovered in China at present belong to lithologic gas reservoirs, with short-distance charging and accumulation, complex pore structures, resulting in diverse gas-water occurrence states. Gas-water differentiation only occurs in some structural positions or fracture-developed areas, and the water production law is complex during the production process, seriously affecting the development effect. The complex gas-water occurrence states lead to continuous changes in gas-water relative permeability, stress sensitivity, etc. during the development process, making it difficult to simulate and characterize.

[0003] In existing research, 202210300381.X provides a numerical simulation method for shale gas reservoirs, establishing a geological modulus-digital simulation integrated coupling model, which improves the recovery rate of shale gas wells. 202411336386.3 discloses a numerical simulation method, device and medium for fluid-solid coupling of shale gas reservoirs considering proppant distribution, establishing a numerical simulation method for shale gas reservoirs considering the actual distribution characteristics of proppants in fractures and the stress sensitivity of the conductivity of the propped fracture area. 202410792120.3 discloses a numerical simulation method for the development of shale condensate gas reservoirs based on the general pEDFM, providing a numerical simulation tool with the best comprehensive calculation performance in theory for the development of fractured shale condensate gas reservoirs. 202010548844.5 discloses a numerical simulation method for the combined production of coalbed methane and tight gas, reducing the total number of model grids, optimizing the model size, and accelerating the operation rate. 202310361157.6 discloses a numerical simulation characterization method for high-multiple water flooding of bottom water reservoirs considering the time-varying relative permeability, improving the time-varying starting endpoint of the time-varying relative permeability technology in current numerical simulations, and making the prediction of water flooding efficiency and ultimate recovery rate in actual oilfield production more accurate.

[0004] However, there is a problem with the above publicly disclosed research results: Tight gas reservoirs generally have characteristics such as low porosity, low permeability, and high water saturation, resulting in special seepage mechanisms such as time-varying relative permeability and stress sensitivity during the gas reservoir development process. However, current traditional commercial software cannot consider the special seepage mechanisms of tight gas, so there will be large errors in the simulation process. Therefore, it is crucial to consider special seepage mechanisms such as time-varying relative permeability and stress sensitivity in the numerical simulation process for the efficient development of tight gas. Summary of the Invention

[0005] To solve the drawbacks of the above existing technologies, the present invention discloses one, and the following technical means are adopted: The present invention provides a numerical simulation method for tight sandstone gas reservoirs considering the time-varying reservoir parameters. Based on the INTERSECT numerical simulator of the commercial software Petrel, combined with the stress sensitivity and the experimental results of gas-water two-phase relative permeability, through Python code, the above experimental results are imported into the INTERSECT numerical simulator to establish a numerical simulation method for tight sandstone gas reservoirs considering complex seepage mechanisms such as stress sensitivity and time-varying relative permeability.

[0006] To achieve the above object, the present invention provides a numerical simulation method for tight sandstone gas reservoirs considering the time-varying reservoir parameters, and the following technical means are adopted: A numerical simulation method for tight sandstone gas reservoirs considering the time-varying reservoir parameters. The reservoir parameters of the present invention refer to reservoir permeability and relative permeability. The time-variation of the reservoir parameters is characterized by stress sensitivity and time-varying relative permeability respectively. The simulation method of the present invention includes the following steps: S1. Based on the core samples taken from the gas field to be simulated, construct a stress sensitivity experiment to test the variation law of core permeability with time (i.e., with formation pressure) under the initial permeability and initial water saturation. Wherein, the initial permeability and initial water saturation refer to the initial permeability and initial water saturation of the reservoir of the gas field to be simulated.

[0007] For the specific method of the stress sensitivity experiment, reference can be made to the national standard of the People's Republic of China "GB / T 29172-2012 Core Analysis Method", which will not be elaborated in the present invention.

[0008] S2. Based on the stress sensitivity experiment results of step S1, fit the relationship between core permeability and formation pressure, and the relationship between core permeability and formation pressure is characterized by a mathematical model of the influence of formation pressure on core permeability or a normalized curve of core stress sensitivity. S3. Based on the relationship between core permeability and formation pressure described in step S2, construct a relationship between core permeability and conductivity multiplier. S4. Based on the relationship between core permeability and formation pressure described in step S2 and the relationship between core permeability and conductivity multiplier described in step S3, modify the conductivity multiplier in the rock compressibility table of the Petrel software to achieve the characterization of stress sensitivity. After correcting the conductivity multiplier of the Petrel software by using the method disclosed in the present invention, the subsequent numerical simulation of tight sandstone gas reservoirs will be more accurate. For example, when simulating and predicting the pressure field of the reservoir, the corrected conductivity multiplier takes into account the influence of pressure change on permeability, and the prediction result will be closer to the pressure field change in the actual production process.

[0009] S5: Conduct gas-water two-phase relative permeability experiments under different permeabilities and water saturations using the unsteady state method, and measure the variation law of relative permeability endpoints with time (i.e., formation pressure and permeability) (for the specific experimental method, refer to: Wang Hao, Sun Jianmeng, Cui Ruikang, etc. Data processing method for unsteady state gas-water relative permeability experiment [J]. Well Logging Technology, 2023, 47(02): 161-166. This invention will not elaborate further), and establish the correlation formula between relative permeability endpoints and formation pressure and permeability; S6: Establish the correlation formula between relative permeability endpoints and formation pressure and conductivity multiplier according to the relationship between conductivity multiplier and core permeability; S7: Write Python language code in the INTERSECT numerical simulator of Petrel software, define the output of the properties required for time-varying relative permeability, and output the pressure and conductivity multiplier of each grid at all times after numerical simulation; S8: Write numerical simulation code based on Python, convert the correlation formula between relative permeability endpoints and formation pressure and conductivity multiplier into code language, and put it into the INTERSECT numerical simulator to realize the characterization of time-varying relative permeability in the numerical model.

[0010] By considering the relationship between relative permeability endpoints and formation pressure and conductivity multiplier, this invention corrects the relative permeability endpoints and realizes the correction of time-varying relative permeability by inputting them into the INTERSECT numerical simulator. The subsequent numerical simulation of tight sandstone gas reservoirs will be more accurate. For example, when simulating and predicting the saturation field of the reservoir, using the corrected time-varying relative permeability for prediction, the prediction result will be closer to the saturation field in the actual production process.

[0011] Furthermore, in step S2, the mathematical model of the core permeability affected by formation pressure is: (Ⅰ) In formula (Ⅰ), K is the core permeability, mD; K 0 is the initial permeability of the reservoir, mD; exp is the exponential function with the natural number e as the base; P is the formation pressure; , c are constants; The model of formula (Ⅰ) proposed by this invention is applicable to all tight sandstone gas reservoirs. The difference is that the , c values of different tight sandstone gas reservoirs are different. The , c values of the gas field to be simulated are obtained by substituting the stress sensitivity experiment results in step S1 (i.e., multiple groups of formation pressure and their corresponding permeability data) into the model of formula (Ⅰ).

[0012] Furthermore, in formula (Ⅰ), -1 < <0, 0 < c < 1.

[0013] Furthermore, in step S3, the relationship between the core permeability and the conductivity multiplier is as follows: (Ⅱ) In formula (Ⅱ), K is the core permeability, mD; K e is the core permeability corresponding to substituting the initial formation pressure into the relationship between the core permeability and the formation pressure fitted in step S2, mD; T m is the conductivity multiplier, which is the ratio of the core permeability to K e the ratio.

[0014] The initial formation pressure is the initial formation pressure of the reservoir of the gas field to be simulated.

[0015] Furthermore, the relative permeability endpoints are characterized by the irreducible water saturation. In step S5, the correlation between the relative permeability endpoints, the formation pressure, and the permeability is as follows: (Ⅲ) In formula (Ⅲ), S wc is the irreducible water saturation, %; K is the core permeability, mD; P is the formation pressure, MPa; a, b, c, d are constants; The values of a, b, c, d for the gas field to be simulated are obtained by substituting the experimental results of the gas-water two-phase relative permeability experiments at different permeabilities and water saturations in step S5 into the correlation formula of formula (Ⅲ).

[0016] The model of formula (Ⅲ) proposed by the present invention is applicable to all tight sandstone gas reservoirs. The difference lies in that the values of a, b, c, d for different tight sandstone gas reservoirs are different. The values of a, b, c, d for the gas field to be simulated are obtained by substituting the experimental results (i.e., multiple sets of formation pressure, permeability, and their corresponding irreducible water saturation data) of the gas-water two-phase relative permeability experiments at different permeabilities and water saturations in step S5 into the model of formula (Ⅰ).

[0017] Furthermore, in formula (Ⅲ), -1 < a < 0, 0 < b < 1, -1 < c < 0, 0 < d < 1.

[0018] Compared with the prior art, the beneficial effects of the present invention are: Based on commercial reservoir numerical simulation software, according to the characteristics of tight high-water-bearing tight sandstone gas reservoirs, combined with core stress sensitivity experiments and core gas-water two-phase relative permeability experiments, a time-varying relative permeability model with relevant improvements made to the relative permeability endpoints is established. Considering that stress sensitivity and time-varying relative permeability endpoints in numerical simulation have higher prediction accuracy for indicators such as decline rate and recovery rate, it provides a theoretical basis for the research and exploitation of residual gas in gas fields.

[0019] The present invention establishes a numerical simulation method for tight sandstone gas reservoirs considering the time-variation of reservoir parameters based on commercial software, clarifies the influence of stress sensitivity and time-varying relative permeability effects on the reservoir pressure field and saturation field, provides a theoretical basis for analyzing the reservoir pressure drop law, saturation change law, and production decline change law, and makes the recovery rate prediction and residual gas distribution more consistent with the actual oilfield production. Brief Description of the Drawings

[0020] Figure 1 It is the standardized curve of core stress sensitivity for Example 1; Figure 2 It is the curve of irreducible water saturation changing with formation pressure; Figure 3 It is the comparison diagram of formation pressure fields before and after considering the time-variation of reservoir parameters; Figure 4 It is the comparison diagram of water saturation fields before and after considering the time-variation of reservoir parameters; Figure 5 It is the curve of irreducible water saturation changing at different development times; Figure 6 It is the flow chart of the numerical simulation method for tight sandstone gas reservoirs in Example 1. Detailed Embodiments

[0021] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings.

[0022] Example 1 Taking a well block in Gas Field D in the Ordos Basin as an example, the initial formation pressure of this well block is 28.5 MPa, the initial formation permeability is 0.13 mD, the porosity is 28%, and the initial formation water saturation is 60%.

[0023] As Figure 6 shown, the present embodiment discloses a numerical simulation method for tight sandstone gas reservoirs considering the time-variation of reservoir parameters, including the following steps: S1. Based on the core samples taken from this well block in Gas Field D, build a stress sensitivity experimental device, and measure the variation law of core permeability with time (i.e., with formation pressure) under the initial formation permeability and initial water saturation; S2. Based on the core stress sensitivity experimental results in step S1, establish a mathematical model for the influence of formation pressure on core permeability in this well block through a fitting relationship:

[0024] and the normalized core stress sensitivity curve of this well area, as Figure 1 shown.

[0025] S3. According to the mathematical model in step S2 or Figure 1 , define the conductivity multiplier ( T m ) at the original formation pressure (28.5 MPa) of the reservoir as 1, calculate the ratio of the permeability at different formation pressures to the permeability at the original formation pressure of the reservoir (i.e., the conductivity multiplier) when the water saturation is 60%, and regress the relationship between the conductivity multiplier and the permeability:

[0026] S4. Based on the results of steps S2 and S3, set the conductivity multipliers at different formation pressures in the rock compressibility table (Table 1) of Petrel software to achieve stress sensitivity characterization. Petrel software can fit the relationship between the formation pressure and the conductivity multiplier based on the rock compressibility table.

[0027] Table 1 Rock compressibility table

[0028] S5. Use the unsteady state method to carry out gas-water two-phase relative permeability experiments at different permeabilities and water saturations, and study the variation law of irreducible water saturation with formation pressure at different permeabilities (as Figure 2 shown, Figure 2 an exemplary curve is given), and further establish the correlation between irreducible water saturation, formation pressure and permeability:

[0029] S6. Couple the relationship between the conductivity multiplier and the permeability (obtained in step S3) into the correlation between irreducible water saturation, formation pressure and permeability obtained in step S5 to obtain the correlation between irreducible water saturation, formation pressure and conductivity multiplier:

[0030] S7. Write Python language code in the INTERSECT numerical simulator of Petrel software to obtain the pressure and conductivity multiplier of the model at each time step during the numerical simulation process.

[0031] S8. Write Python language code in the INTERSECT numerical simulator, convert the correlation between irreducible water saturation and formation pressure and conductivity into code language, and use the pressure and conductivity multipliers obtained in step 7 to calculate the irreducible water saturation of the next time step, and write the calculated irreducible water saturation into the numerical simulation model to replace the original irreducible water saturation. Update the irreducible water saturation once every time step to realize the characterization of the time-varying phase permeability in the numerical simulation model of the well area.

[0032] S9. Use the above numerical simulation model (i.e., the simulation model after correcting the conductivity multiplier and irreducible water saturation in the simulation model provided by the software) to calculate the results of the well area after 5 years of development, and compare them with the results without considering the time-varying reservoir parameters to analyze the pressure field after 5 years of development (such as Figure 3 As shown in Figure 2), water saturation field (as shown in Figure 2), Figure 4 ) and the differences in bound water saturation during development (e.g. Figure 5 The changing pattern of ).

[0033] in, Figure 3 The left side in the middle shows the pressure field without considering the time-varying reservoir parameters, and the back side shows the pressure field with considering the time-varying reservoir parameters. Figure 4 The left side in the middle shows the water saturation field without considering the time-varying reservoir parameters, and the back side shows the water saturation field with considering the time-varying reservoir parameters. Figure 5 It can be seen that when the time-varying reservoir parameters are not considered, the irreducible water saturation remains unchanged. After the time-varying reservoir parameters are considered, the irreducible water saturation tends to increase with the increase of development years, which is closer to the actual state of the tight sandstone gas reservoir during exploitation.

Claims

1. A numerical simulation method for tight sandstone gas reservoirs considering the time-varying reservoir parameters, characterized in that, It includes the following steps: S1. Based on the core samples taken from the field of the gas field to be simulated, construct a stress sensitivity experiment to test the variation law of core permeability with time under the initial permeability and initial water saturation; S2. Based on the stress sensitivity experiment results in step S1, fit the relationship between core permeability and formation pressure, and the relationship between core permeability and formation pressure is characterized by a mathematical model of the influence of formation pressure on core permeability or a normalized curve of core stress sensitivity; S3. Based on the relationship between core permeability and formation pressure described in step S2, construct a relational expression between core permeability and conductivity multiplier; S4. Based on the relationship between core permeability and formation pressure described in step S2 and the relational expression between core permeability and conductivity multiplier described in step S3, modify the conductivity multiplier in the rock compressibility table of Petrel software to achieve the characterization of stress sensitivity; S5: Use the unsteady state method to carry out gas-water two-phase relative permeability experiments under different permeabilities and water saturations, determine the variation law of relative permeability endpoints with time, and establish a relational expression between relative permeability endpoints, formation pressure and permeability; S6: Establish a relational expression between relative permeability endpoints, formation pressure and conductivity multiplier according to the relationship between conductivity multiplier and core permeability; S7: Write Python language code in the INTERSECT numerical simulator of Petrel software, define the output of the properties required for time-varying relative permeability, and output the pressure and conductivity multiplier of each grid at all times after numerical simulation; S8: Write numerical simulation code based on Python, convert the relational expression between relative permeability endpoints, formation pressure and conductivity multiplier into code language, and put it into the INTERSECT numerical simulator to achieve the characterization of time-varying relative permeability in the numerical model.

2. The numerical simulation method for tight sandstone gas reservoirs considering the time-variation of reservoir parameters according to claim 1, characterized in that In step S2, the mathematical model of the influence of formation pressure on core permeability is: （Ⅰ） In formula (I), K is the core permeability, mD; K 0 is the initial reservoir permeability, mD; exp is the exponential function with the natural number e as the base; P is the formation pressure; , c are constants; The , c value of the gas field to be simulated is obtained by substituting the stress sensitivity experiment results of S1 into the model of Equation (Ⅰ).

3. The numerical simulation method for tight sandstone gas reservoirs considering the time-variation of reservoir parameters according to claim 2, characterized in that, In formula (I), -1 < < 0, 0 < c < 1.

4. The numerical simulation method for tight sandstone gas reservoir considering the time variation of reservoir parameters according to claim 1, wherein In step S3, the relational expression between core permeability and conductivity multiplier is: （Ⅱ） In formula (II), K is the core permeability, mD; K e is the core permeability corresponding to bringing the initial formation pressure into the relationship between the core permeability and the formation pressure fitted in step S2, mD; T m is the conductivity multiplier.

5. The numerical simulation method for a tight sandstone gas reservoir considering the time variation of reservoir parameters according to claim 1, characterized in that, The relative permeability endpoints are characterized by irreducible water saturation; In step S5, the relational expression between relative permeability endpoints, formation pressure and permeability is: （Ⅲ） In formula (III), S wc is the irreducible water saturation, %; K is the core permeability, mD; P is the formation pressure, MPa; a, b, c, and d are constants; The values of a, b, c, and d of the gas field to be simulated are obtained by substituting the experimental results of the gas-water two-phase relative permeability experiments under different permeabilities and water saturations in step S5 into the relational expression of formula (Ⅲ).

6. The numerical simulation method for tight sandstone gas reservoirs considering the time-variation of reservoir parameters according to claim 5, characterized in that, In formula (Ⅲ), -1 < a < 0, 0 < b < 1, -1 < c < 0, 0 < d < 1.

7. A numerical simulation method for a tight sandstone gas reservoir considering the time-variation of reservoir parameters according to claim 1, characterized in that: The time variation of the reservoir parameters includes stress sensitivity and time-varying relative permeability.

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